Re: Formula Stirlinga

*To*: mathgroup at smc.vnet.net*Subject*: [mg130705] Re: Formula Stirlinga*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sat, 4 May 2013 03:17:41 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

On 5/1/13 at 9:43 PM, karchevskymi at gmail.com wrote: >n = 1000; N[n! - Sqrt[2*Pi*n]*(n/Exp[1])^n] = 3.35308734163*10^2563 >Why does Stirling's formula works incorrect? Stirling's formula is a valid approximation. But the way you are trying to demonstrate that isn't effective. Note In[1]:= n = 1000; N[(Sqrt[2*Pi*n]*(n/E)^n)/n!] Out[2]= 0.999917 In[3]:= 100 (1 - %) Out[3]= 0.00833299 That is there is an error of about 0.008% and In[4]:= Log[10, n!] + Log[10, %/100] Out[4]= 2563.53 That is an error of 0.008 amounts to a difference of 10^2563